A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. If he is willing to assume that these rates are randomly drawn from a normally distributed population, can he conclude that the mean mortgage rate for the population exceeds 4.20%? Test the hypothesis at a 10% level of significance. (You may find it useful to reference the appropriate table: z table or t table) Financial InstitutionAPR G Squared Financial 4.255% Best Possible Mortgage 4.265 Hersch Financial Group 4.200 Total Mortgages Services 4.540 Wells Fargo 4.175 Quicken Loans 4.225 Amerisave 4.490 Source: MSN Money.com; data retrieved October 1, 2010. Click here for the Excel Data File a. Select the null and the alternative hypotheses. multiple choice 1H0: µ ≥ 4.20; HA: µ < 4.20H0: µ ≤ 4.20; HA: µ > 4.20H0: μ = 4.20; HA: μ ≠ 4.20 b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

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Description: A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. If he is willing to assume that these rat

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A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. If he is willing to assume that these rates are randomly drawn from a normally distributed population, can he conclude that the mean mortgage rate for the population exceeds 4.20%? Test the hypothesis at a 10% level of significance. (You may find it useful to reference the appropriate table: z table or t table)

Financial Institution	APR
G Squared Financial		4.255	%
Best Possible Mortgage		4.265
Hersch Financial Group		4.200
Total Mortgages Services		4.540
Wells Fargo		4.175
Quicken Loans		4.225
Amerisave		4.490

Source: MSN Money.com; data retrieved October 1, 2010.

Click here for the Excel Data File

a. Select the null and the alternative hypotheses.

multiple choice 1

H₀: µ ≥ 4.20; H_A: µ < 4.20
H₀: µ ≤ 4.20; H_A: µ > 4.20
H₀: μ = 4.20; H_A: μ ≠ 4.20

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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